Some series do not step by a fixed amount or multiply by a fixed factor. Each term is made from the ones just before it. The most famous example is the Fibonacci sequence, and it turns up, in disguise, in a lot of number series tests.
The rule in one line
Start with two numbers. Each new number is the sum of the previous two. 1, 1, 2, 3, 5, 8, 13, ? gives 8 + 13 = 21. The sequence is named after Leonardo of Pisa, known as Fibonacci, who described it in a book written in 1202.
The famous sequence starts 1, 1, but the rule does not care where you start. 2, 3, 5, 8, 13, 21, ? is the same rule from different seeds, and the answer is 34. So is 3, 4, 7, 11, 18, 29, ?, where 18 + 29 gives 47.
The giveaway: the gaps are the series again
Take the gaps of 2, 3, 5, 8, 13, 21 and you get 1, 2, 3, 5, 8. That is the same list, shifted one place. It happens because each term minus the one before it is exactly the term before that.
So if the gaps look like the series you started with, stop looking for a gap rule and check whether each term is the sum of the previous two. The next gap here is 13, and 21 + 13 gives 34.
The three-term version
A harder cousin adds the three terms before. 1, 2, 4, 7, 13, 24, ? works like this: 1 + 2 + 4 = 7, 2 + 4 + 7 = 13, 4 + 7 + 13 = 24, so the next term is 7 + 13 + 24 = 44.
Starting elsewhere changes how it looks. 3, 1, 2, 6, 9, 17, ? is the same rule: 3 + 1 + 2 = 6, 1 + 2 + 6 = 9, 2 + 6 + 9 = 17, so the next term is 6 + 9 + 17 = 32. The row is not sorted and the first gap is negative, which hides the rule from anyone who only reads gaps.
A two-second test
Check the third number first. Is it the first plus the second? If yes, check the fourth against the second plus the third. Two matches in a row is a strong sign. If not, try the first three summed against the fourth.
Do not decide on a single match. 2, 3, 5 fits the sum rule, but it also fits "add 1, add 2". It is the fourth and fifth terms that settle it, which is why the check has to run along the whole row.
Why these items feel hard
Gap-spotting is the habit most people learn, and it is the one that misleads here: the gaps are irregular, the ratios are irregular, and nothing looks like a staircase. The rule is only visible when you look at each term in relation to the two or three behind it.
On the JobCannon Number Series test these sit in the chained-rules group, alongside double-then-adjust patterns. If your results are weakest there, it is often this single move that is missing, and it is quick to learn. The number series practice page lists extra series of the same type, and the JobCannon Numerical Reasoning test is where the wider arithmetic skills live.